I want to change change the arrangement of the grid of posts displayed by the theme on the Search page (read the description for better understanding)

Try using flexbox, try adding the following in your custom CSS. Here is more info on flexbox and a flexbox generator you can play around with.

    .grid-wrapper {
        display: -ms-flexbox;
        display: -webkit-flex;
        display: flex;
        -webkit-flex-wrap: wrap;
        -ms-flex-wrap: wrap;
        flex-wrap: wrap;
    }